Pazu was working for coal miners when a girl floated down from the sky wearing a glowing green pendant. Her name was Sheeta, and she was on the run from people after that pendant around her neck. Pazu decides to help her, and at the same time go on his own quest for the floating city of Laputa, which his father glimpsed briefly before his death. However, there are pirates after the crystal on the pendant, and someone working for the military wants to use it to find the floating city as well. Who will gain control of the crystal, and what secrets lie in the castle in the sky?
This is my favorite Miyazaki movie. I'm not quite sure what puts it above the rest that I've seen, but there's something, darn it. I think it may be that it's the most... normal? world he's made (and that doesn't mean this doesn't have its fair share of fantasy in it). I think it's the most realistic. In any case, the plot is straightforward, though it drags a little in the middle, and not much, and it has a definite conclusion. Can't say whether it's satisfying or not... it will depend on your tastes.
The soundtrack for this, like all of Miyazaki's other movies, as far as I know, was done by Joe Hisaishi, who I place on the same level as John Williams (for those who care about such things), and his soundtracks are consistantly amazing. The characters are likeable if they're supposed to be, and they're hateable if they're supposed to be. There's nothing here to misunderstand.
There ya have it. Thanks for watching!